Design and Computational Modeling of Fabric Soft Pneumatic Actuators for Wearable Assistive Devices Pham Huy Nguyen & Wenlong Zhang✉

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OPEN Design and Computational Modeling of Fabric Soft Pneumatic Actuators for Wearable Assistive Devices Pham Huy Nguyen & Wenlong Zhang✉

Assistive wearable soft robotic systems have recently made a surge in the feld of biomedical robotics, as soft materials allow safe and transparent interactions between the users and devices. A recent interest in the feld of soft pneumatic actuators (SPAs) has been the introduction of a new class of actuators called fabric soft pneumatic actuators (FSPAs). These actuators exploit the unique capabilities of diferent woven and knit textiles, including zero initial stifness, full collapsibility, high power- to-weight ratio, puncture resistant, and high stretchability. By using 2D manufacturing methods we are able to create actuators that can extend, contract, twist, bend, and perform a combination of these motions in 3D space. This paper presents a comprehensive simulation and design tool for various types of FSPAs using fnite element method (FEM) models. The FEM models are developed and experimentally validated, in order to capture the complex non-linear behavior of individual actuators optimized for free displacement and blocked force, applicable for wearable assistive tasks.

In the recent years, soft robotics has emerged as a candidate to create novel robotic systems with pre-programmable capabilities, while capable of withstanding large deformations. Tese systems have shown to be potentially useful in diverse application felds ranging from bio-inspired robotic systems1,2, adaptable locomotion in unstructured environments1,3, grasping/manipulation of objects4, invasive surgical instruments5 and assistive/rehabilitative devices6. Tese intrinsically sof robots have advantages over conventional rigid robots by being low-cost, lightweight, highly compliant, and inherently safe when interacting with the unknown environment and human body2,6. Terefore, these sof robots can be utilized for rehabilitation, prevention of injuries, or augmentation of the capabilities of healty individuals6,7. Sof wearable assistive/rehabilitative robots are generally categorized based on the joints they assist as well as the type of actuators actuators utilized to design them6. Upper-body sof wearable robots have been developed to actively support fngers8–13, wrists14, elbows15,16, shoulders17–19, necks20, forearms21,22, and spines23,24. Lower-body sof wearable robots have provided assistance to the hips25, knees26,27, and ankles28–31. Common sof actuation methods for assistive/rehabilitative tasks include cable-driven11,14,25, origami32,33, and sof pneumatic actuators (SPAs)2,6,34. SPAs broadly categorizes sof actuators that require positive or negative pressure to generate pre-programmable motion2,6,34. Pneumatic artifcial muscles20,29, elastomeric10,23,35 and infatable fabric sof pneumatic actuators (FSPAs) all fall under this category9,13,18,19,21,22,26–28,36,37. SPAs can also be further classifed according to how they are mechanically programmed to move whether in the macro or micro-scale2,6,34. Teir motion paths can be programmed using combinations of multiple infatable chambers or actuators as seen with peano muscles and bellow actuators15,37–50. A form of external/internal fexible mechanical metamaterials51 (for example, rein- forcements6,34,52–54 and auxetic structures55–58) or origami structures32,33,59–62 can also be used for mechanical programmable motions. Te programmable motions include2,6,34,42,54,63: twisting64,65, bending39,50, stifening26,28, contracting30,39,41,44,46,66, or extending/growing67–70 in space. Further, by combining multiple actuators together in a modular unit, a continuum, multi-chambered and multi-DOF actuator can be created38,50,71,72.

The Polytechnic School, Ira A. Fulton Schools of Engineering, Arizona State University, Mesa, AZ, 85212, USA. ✉e-mail: [email protected]

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Figure 1. (a) Illustrated concept of the knit stretch FSPAs. (b) Illustrated concept of the woven non-stretch FSPAs. (c) Illustrated concept of the various wearable assistive applications using FSPAs.

Te development of wearable technologies has generated a lot of interest in the use of textiles or fabrics, both terms used interchangeably in this work, due to their versatility, repeatable production, and omnipresent nature73. Fabrics have also shown to be a promising medium to incorporate functionalities like: sof computing, fexible electronics, energy harvesting, sensing and actuation73. Sof fabric actuation has shown possibilities of utilizing fabric to generate movement and provide assistance74. Te construction of these fabric actuators has been through either intrinsic or extrinsic modifcations of the materials74. Wearable assistive devices have seen a growth in utilizing extrinsically-modifed fabric actuation technol- ogy9,13,16,28,36,37. Extrinsically-modifed fabric actuators, are fabricated by superfcially attaching active materials on the surface of the substrate fabric, for example laminating thermoplastic polyurethane (TPU) material on the substrate fabric to create FSPAs73,74. Tis paradigm shif has lead to design of SPAs that are easily integrated with or hidden underneath the users’ clothes. Along with the ease of fabrication, wearability, pliability, and availability, these actuators also provide enough torque and force assistance to the extremity, making this technology more adoptable for everyday life8,9,12,13,15–18,21,22,26,28,31,37,75. FSPAs are further classifed based on the types of fabrics used to make them. In this work, we focus on two categories of extrinsically modifed FSPAs, woven and knit FSPAs, shown in Fig. 1a,b. Because of how each type of fabric material is manufactured, woven fabrics are generally puncture resistant but less deformable, while knit fabrics are easily deformable and have an innate mechanical anisotropy (showing variable stretchability in bi-directions)73. Recent research have seen woven fabrics used to create highly robust twisting, contracting and bending actuators12,13,15,18,19,24,27–31,37,43,50,75, as well as the use of the knit textiles to create bending actuators for grippers and wearable robots8,9,76. Tere have been various computational and analytical studies on the prediction of fabric properties at the fber or yarn level, but not for the entire set of the fabric structural hierarchy73. Only recently have models for woven FSPAs been developed to predict their force and motion capabilities8,22,28. Our preliminary work has shown prom- ise in utilizing computational models for woven FSPAs for the elbow15 and also continuum assistive robots50. On the other side of the spectrum, modeling of knit FSPAs are still in the nascent phase of development8,9. In this paper, we further investigate the combination of various textile layers to mechanically program actuators in order to perform various motion profles, as highlighted in previous work15,24,26,36,50,75. Specifcally, two categories of multi-material and multi-layered woven and knit FSPAs as shown in Fig. 1, are studied and fabricated. A comprehensive material study of both the various woven and knit anisotropic textiles are conducted for large deformations to generate material models. To accurately predict the complex mechanical response of the FSPAs, we opt to create computational fnite element method (FEM) models. Computational FEM models have the ability to generate detailed models, based on the actuator’s variable geometrical parameters non-linear behaviors and capture the detailed stress-strain distributions of multi-material and multi-layered7,23,77. We develop an all-inclusive design tool using the computational models, that will benchmark the design criteria for developing a new robust woven or knit fabric actuator based on the desired geometrical parameters and application force/

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Figure 2. (a) Machines used for fabrication (b) Layout of fabrics cut using a laser cutter (c) Fabrication procedure of internal TPU bladder (d) Fabrication procedure of knit stretch FRTA for bending. (e) Fabrication procedure of knit Stretch FRTA for twisting and extending. (f) Fabrication procedure for woven fabric actuators. (g) Microscope view and illustration of the yarns in the woven fabric. (h) Microscope view and illustration of the yarns in the knit stretch fabric.

torque requirements. Tis comprehensive tool will allow for scalability and customizability of diverse FSPAs prior to fabrication. Design and Fabrication of the FSPAs Te two main fabrics used in this work include, the woven non-stretch thermoplastic polyurethane (TPU)-coated nylon fabric (6607, Rockywoods Fabric, Loveland, CO) and the bi-directional high-stretch knitted fabric (24350, Darlington Fabrics, Westerly, RI). Both fabrics are seen under a microscope (OMAX A355U, OMAX Microscope, Seattle, WA) with a magnifcation factor of 40× and numerical aperture of 0.65, as shown in Fig. 2g, h. Te two directions of stretch include the wale (in the y-direction) and the course (in the x-direction). Woven fabrics are generally created with vertical (warp) yarns interlaced with horizontal (wef) yarns in a checkered pattern, as seen in Fig. 2g73. Material properties of woven fabrics are dependent on the strain properties

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of the yarns used to create them. Te nature of the weaving method, creates a tight interconnected thread system resulting in a more stable, rigid, and difcult to deform fabric73. On the other hand, knit fabrics are created by the interlocking loops of a single yarn (i.e. wef knits) or multiple yarns (i.e. warp knits)73. Te knitted fabric used in this work, is created by using a warp knitting. Te fabric is made of 83% semi-dull nylon and 17% spandex. Tis essentially means that warp knits ofen have mechanical anisotropy, because one stretch direction is relatively stretchier than the other (the preferential strain direction), as seen in Fig. 2h. Tus, the knit fabrics show high bi-directional stretchability and elastic recovery, comparable to the hyperelastic properties of elastomers. Tese woven and knit fabrics are used to create two categories of FSPAs: woven FSPAs highlighted in Fig. 1a, and knit fabric-reinforced textile actuators (FRTAs) as highlighted in Fig. 1b. Te woven non-stretch fabric actuators generate motion by combining multiple pouch fabric actuators, that infate to a set size, in various array for- mations, to contract, straighten, bend, or elongate. In contrast, the knitted FRTAs are developed by combining an internal knit fabric shell with strain-limiting woven fabric reinforcement layers, so the fabric’s overall anisotropic behavior can be augmented during pressurization. Further, the woven fabric reinforcements also reduce the local stresses and strains on the internal shell and minimizes any surface damage, from abrasion commonly seen with the use of Kevlar threads as reinforcements, seen in previous work6. Finally, by arranging multiple actuators in diferent orientations we can also create multiple degree-of-freedom (DOF) actuators, as shown in Fig. 1. Tese various types of actuators generate motion profles that can serve various target applications in the feld of wearable assistive devices as featured in Fig. 1c and further mentioned in Supplementary Table 1.

Fabrication of the FSPAs. Te machines used in the fabrication procedure are shown in Fig. 2a. Te laser-cutter (Glowforge Prof, Glowforge, Seattle, WA) is used to cut all the TPU (Fastelflm 20093, Fastel Adhesive, Clemente, CA), woven and knit fabrics into the desired geometry, as shown in Fig. 2b. Te TPU sheets are used to bond the knit fabric and the woven fabric reinforcements, while coating the knit fabric substrate to make it airtight. However, air leakage through the skin of the fabric is still noticed. Terefore, an additional airtight TPU bladder with a pneumatic connector (5463K361, McMaster-Carr, Elmhurst, IL), is still made using an impulse sealer (751143, Metronic, Seattle, WA) as seen in Fig. 2c. Tere are two variations of fabricating the FRTAs, one for FRTAs that perform bending, in Fig. 2d, and the other FRTAs that elongate and/or twist, as shown in Fig. 2e. In the frst variation of the fabrication method the knit stretch fabric, a single TPU sheet, and woven TPU-coated reinforcements are assembled and bonded all at once using a heat press (FLHP 3802, FancierStudio, Hayward, CA). Te TPU bladder is placed in the middle of the prepared multi-layered fabric set, and the structure is folded and sewn, using a super-imposed seam along the center. Te sewn portion creates the strain-limiting, inextensible seam to encourage bending towards that particular direction. In the second variation of the fabrication method, two sets of knit stretch fabric and woven reinforcements are created. Te additional TPU bladder is placed between the two sets of multi-layered fabric sets and the edges of the layers are heat-sealed or sewn along the edges using high-stretch elastic thread (Maxi Lock Stretch, American & Efrd, Mount Holly, NC). Diferent clockwise/counterclockwise twisting and elongating actuators can be developed by varying the angle of woven reinforcements. In order to fabricate the woven FSPAs, the TPU-coated nylon fabric is cut into the desired geometries as seen in Fig. 2f. Te woven TPU-coated nylon already has a side pre-laminated with a TPU coating to allow bonding. Pneumatic fttings are attached to the cutouts and aligned on the bed of the customized computer numerical control (CNC) router (Shapeoko 3, Carbide Motion, Torrance, CA) with a soldering iron tip set at 230 °C. Te CNC router traces and seals the fabric cutouts to seal the individual fabric actuators. Tis procedure can instantly create the woven straightening or contracting FSPAs. In order to create the woven bending and elongating FSPAs, pouches with the same size as the actuators are created. Te pouches are sewn together using a sewing machine (Memory Craf 6500 P, Janome, Hachioji, Tokyo) to create the actuator array structure for the sealed actuators to slot into. If the pouches are sewn one on top of each other, elongation actuators are created. If the pouches are sewn along the base onto a strain-limiting inextensible layer, the bending actuators are created, as seen in Fig. 2f. Finally, the manufacturing procedure for the multi-DOF continuum actuators, as seen in Supplementary Video 4, is discussed in Supplementary Materials. Constitutive Material Model Fitting of Fabrics and Textiles We try to identify the appropriate material model parameters for the diferent textiles and fabrics we use as a pre- cursor for the proposed FEM models. In Supplementary Materials, we further described the geometrical parameters, as shown in Fig. 3a–f, and experimental procedure for characterizing the diferent woven non-stretch and knitted stretch fabrics using uniaxial and/or biaxial universal tensile testing machines, as shown in Fig. 3g,h. We note that the material properties of the TPU-coated materials are within the elastic range while the properties of the knit stretch fabric is considered as an anisotropic hyperelastic material. Previous FEM-based sof robot modeling work has focused on isotropic elastomeric materials7,77. Material properties of these actuators and robots were captured using Arruda-Boyce, Van-der-Waals, Mooney-Rivlin and Neo-Hookean models for smaller strains7, and Ogden, Yeoh, and higher-polynomial models for larger hyperelastic strains78. However, there have been only one preliminary example of computationally modeling the behavior of knit FSPAs9. In this work, we further model the behavior of multi-layered, multi-material (made of woven fabric reinforcements and a knit fabric shell) FRTAs. Some of the constitutive models included in ABAQUS (Simulia, Dassault Systemes) to model anisotropic models include generalized Fung and Holzapfel-Gasser-Ogden (HGO) models. Te material properties of the TPU-coated nylon are within the elastic range, and the Young’s modulus and Poisson’s ratio are calculated as E = 498 MPa and 0.35 using a uniaxial tensile test as seen in Fig. 3g. Te inextensible fabric layer used to hold the actuators in the actuator array has the properties E = 305 MPa, v = 0.35 and the

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Figure 3. Geometrical parameters for (a) woven contracting actuator, (b) woven extending actuator, (c) woven bending actuator, (d) woven multi-DOF actuator, (e) FRTA actuators, and (f) FRTA multi-DOF actuators. (g) Uniaxial tensile test of woven TPU-coated and knitted stretch fabric. (h) Biaxial Tensile test of bidirectional knitted stretch fabric.

properties used for the PLA connector caps (E = 3600 MPa, v = 0.3). All the components are modeled using shell explicit quadratic tetrahedral elements (C3D10M).

Anisotropic material model of bi-directional textile materials. Te anisotropic hyperelastic properties are evaluated with the HGO continuum model79. A non-linear regression model (Limited-memory BFGS77) was used to ft material data against HGO hyperelastic strain energy function (see Supplementary Materials for more details). Te strain energy equation of the HGO model is as shown below:

 el 2  N 2 1(J )1− el k kE UC=−(3I ) +⋅ − lnJ  +−1 e 2 α 1, 10 1   ∑ D  22 k21α= (1)

EIαα= κκ( 1 −+−3) (1 3 )(I α − 1), (2)

where C10,,Dk12,,k and κ are the fve temperature-dependent material parameters. N is the number of families of fbers (N ≤ 3); I1 is the frst invariant of the Cauchy-Green tensor, I4,6 are the invariants that represent the pre- ferred directions for the fbers contributing to the strain-energy function. If κ (0 ≤≤κ 1 ) is close to 0, it means 3 the fbers are in the direction of θ (the course direction); if κ is close to 1/3, it means the fbers are dispersed and the material would be considered isotropic. Te material ftting tool allows the user to set the poisson ratio, boundary conditions and initial parameters for the material parameters (C10,,Dk12,,k and κ) and the experimental equibiaxial testing data. Te Cauchy stress (σθθ, σzz) is in the course and wale directions. A least-squares ft for the stress-strain equations of both directions is used:

n  2  model model 2 χσ= ∑  θθ − σσθθ  +−()zz σzz ].   i i=1 i (3)

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Te material ftting toolkit also allows the use of multiple optimziation algorithms, such as Nelder-Mead, Powell, CG, L-BFGS-B, COBYLA, and SLSQP, given by the SciPy optimization function77. For every iteration, the coefcient of determination R2 and root mean square of the reduced chi-square ε were used against the material testing data for the next optimization loop. For the equibiaxial protocol80, results were considered acceptable for R2 >.08 and ε >.025. Afer optimization using this scheme, the HGO model is used to ft four tensile testing data sets, two equibiaxial and two uniaxial, as seen in Fig. 3g,h. Te same stretch fabric was used for all tests, one set was coated with a TPU layer to aid bonding and air impermeability and another set was not coated with a TPU layer. For the uncoated uniaxial test, the parameters were identifed as C10 = 1 .156, k1 = 0.0925, k2 = 00. , α = 0.321 and κ = 00. (the R2 =.076 and ε =.028). For the coated uniaxial test, the parameters were identifed as −12 2 C10 =1 .0, k1 = 0.163, k2 = 00. , α =.1931× 0 and κ =.0 133 (the R =.097 and ε =.014). For the uncoated equibiaxial test, the parameters were identifed as C10 = 0.503, k1 = 0.138, k2 = 00. , α =.00 and κ = 00. , with a resultant R2 =.088 and ε =.022. For the coated equibiaxial test, the parameters were −10 2 C10 =1 .098, k1 = 0.225, k2 = 4.−05e 10, α = 00. and κ = 2.×087 10 with a resultant R =.08 and ε =.022. Modeling of fabric-based actuators using FEM(iv) In this work, computational FEM models are created to capture the performance of the various fabric-based actuators. Te efects of their geometrical parameters, highlighted in Fig. 3a–f) and Supplementary Materials, are studied for blocked force and displacement tests using the computational FEM modeling tool written in Python 2.7, for ABAQUS/Explicit (Simulia, Dassault Systemes). Te modeling tool is capable of automating the process of creating the part, meshing, and applying boundary conditions based on the user-defned parameters. Computational models enable rapid design iterations prior to actual fabrication of the prototypes. ABAQUS/Explicit is used to capture the short dynamic response times observed among diferent types of fabric actuators. ABAQUS/Explicit is also capable providing both dynamic and quasi-static solutions for blocked force and displacement tests of the diferent types of actuators. In order to perform quasi-static simulations, the explicit solution would need to be accelerated while still maintaining its dynamic equilibrium81. To maintain dynamic equilibrium the loading rate of the analysis needs to be 1% of the speed of the stress wave of the mate- rial81. To monitor dynamic equilibrium, the total kinetic (KE) and internal (IE) energy of the entire system are monitored to ensure that KE does not exceed 5% of total IE81. Te airfow dynamics within the chambers is disregarded and modeled as pressure equally applied on the actuators’ internal surfaces. Te pressure is designed as a smooth ramp step to the desired value. Gravity is not considered in the models due to the lightweight nature of the actuators. In order to measure the displacement of the actuators, passive refective markers are attached on the fabric actuators during experiments. For measuring bending angle, three markers are distributed evenly along the length of the actuator. For measuring displacements in the three axes, markers are placed at the distal and prox- imal ends of the actuators. A motion capture system (Optitrack Prime 13 W, NaturalPoint Inc., Corvallis, OR) is used for experiments, and each experiment was repeated three times. For measuring the payload of the actuators, we denoted the experimental setup in Supplementary Fig. 3.

FEM models for woven fabric actuators. Computational models for diferent woven non-stretch fabric actuators including the stiffening, contracting, elongating, bending are developed. Figure 4a–d and Supplementary Video 1, shows the Von Mises stress contour plots obtained from the FEM simulations, along with the experimental results of the pressurized actuators at the corresponding input pressure. Te force output (payload) and displacement (bending angle, extension, or contraction) are measured at small pressure increments of 0.034 MPa until a safe operating pressure of 0.206 MPa. Te stifening actuators are used for applications that require an extension motion, such as assisting the knee, wrist, elbow, and fnger joints. Comparison test between the FEM model and experimental prototype is conducted for an actuator with an wa = 65 mm and an Li = 240 mm. For the block force experiments, the actuator was positioned at a desired bending angle of 60° and 90°. Te simulation shows similar performance for the 60 angle with an RMSE of 1.08N, and for the 90 angle with an RMSE of 1.71N, as shown in Fig. 4e. The contracting actuators are used for applications that require pulling or contracting. The geometrical parameters of the actuator used include, na = 7, Li = 200 mm, wa = 60 mm, and ha = 22.86 mm, and with a central- ized air passage with a width of 5mm. For the displacement and blocked force tests, the contracting length (d) and pulling contraction force were measured, respectively. For the displacement test, a maximum displacement error of 13.84% and an RMSE error of 2.06mm are noticed, as seen in Fig. 4f. Te blocked force tests for the modules are modeled with both the top and bottom end-plate faces fxed in all directions (encastre) when under external pressure load. Te simulation predicts the force well up to around 0.17 MPa, afer which the simulation shows slightly higher force readings than the experimental results possibly due to slight air leakage in the prototype because of the material being stretched because of pulling forces of around 270 N. Te RSME of 210. 2N and a maximum force error of 11.45% is noticed, as seen in Fig. 4g. Te elongating actuators’ geometrical parameters include, active width (wa) of 62 mm and active height (ha) of 31mm. Experimental data is gathered for a stack of fve actuators (na = 5). Te free displacement is compared to simulation results as seen in Fig. 4h. Te maximum displacement error of 8.52% and the RMSE error of 3.46mm are observed. For the blocked force test seen in Fig. 4i comparing the experiment and simulation, an RMSE of 1.49N is observed. Both free displacement and blocked force simulations show a good prediction of the experimental results.

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Figure 4. Woven non-stretch fabric actuators: FEM v.s. experimental results for (a) stifening actuator, (b) contracting actuator, (c) elongating actuator, and (d) bending actuator. (e) Straightening actuator: load v.s. pressure. (f) Contracting actuator: displacement v.s. pressure. (g) Contracting actuator: load v.s. pressure. (h) Elongating actuator: displacement v.s. pressure. (i) Elongating actuator: load v.s. pressure. (j) Bending actuator: bending angle v.s. pressure. (k) Bending actuator: load v.s. pressure.

Te bending actuators, designed for various fexion applications are tested for bending angle and blocked force, as shown in Fig. 4d. For the displacement and blocked force tests, actuators with n = 13, wa = 41 mm, and ha = 30mm were used. Te results are shown in Fig. 4j and k. For this test, a vertical plate is designed to limit the distal end of actuator from further curling inwards during infation, to maintain bending angles at around 200°, for ease of monitoring and calculating the bending angles. It is noticed that the bending actuator prototype has an initial bending angle because the fttings on each actuator create an initial stifness. However, at around 30–40% of the simulation the FEM model catches up the experimental data where we see results closely match between the simulation and actual experiments. For the blocked force test, the FEM simulation catches up to the experimental data at around the 60–65% of the simulation. Both present similar payload outputs with a RSME of 2.39N.

FEM models for knit bi-directional stretch fabric actuators. Computational models are created to study the efects of the fabric reinforcement on the motion profle of diferent knit stretch FRTAs. Figure 5a-c and Supplementary Video 2 shows the displacement contour plots obtained from the FEM simulations compared with the experimental images of the pressurized actuators at the corresponding pressure values. The main geometrical parameters studied are the number of reinforcements (n) and angle of the fabric reinforcements (α), as seen in Supplementary Fig. 2. Te force output (payload or torque) and displacement (bending angle, twisting angle, or elongation) are measured at small pressure increments for both the FEM simulations and experiments.

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Figure 5. Knitted stretch fabric actuators: FEM v.s. experimental results for (a) bending actuator, (b) elongating actuator, and (c) twisting actuator. (d) Bending actuator: displacement v.s. pressure. (e) Bending actuator: load v.s. pressure. (f) Elongating actuator: displacement v.s. pressure. (g) Elongating actuator: load v.s. pressure. (h) Twisting actuator: twisting angle v.s. pressure. (i) Twisting actuator: torque v.s. pressure.

Te bending FRTAs were tested for bending angles (Fig. 5d and blocked forces (Fig. 5e). For both tests, the  actuator’s geometrical parameters used were Lmi = 155 m, wr =.15mm, α =0 , wi = 40 mm, wz = 14 mm, and nr = 35. We notice for the bending angle test, the results are closely matched between simulation and actual experiments with an RMSE of 101. 6. For the bending FRTA prototype, there was an initial bending angle because the prototype had a small initial stifness. For the load test, the experimental results followed the same trend as the simulation, with an RMSE of 0.4939N. Te elongating FRTAs were tested for displacements (Fig. 5f and blocked forces (Fig. 5g). Te actuator’s  geometrical parameters used for both tests were Lmi = 155 m, wr =.60mm, α =0 , wi = 46 mm, wz =.00mm, and nr = 15. From the displacement graph, Fig. 5f, we notice that the FEM model matches the experimental data with an RMSE of 1.36 mm. For the blocked force graph, Fig. 5g, the FEM model predicts the payload of the actuator very closely with an RMSE of 5.81N. For the elongating FRTA, the fabric reinforcements convert the radial expansion to axial extension, therefore a higher the number of reinforcement leads to less radial expansion and more elongation. Te twisting FRTA models were experimentally validated for twisting angles and torque capability, as shown in Fig. 5h, i. Te actuator was infated to 0.11 MPa with increments of 0.014 MPa, which was selected as a safe maximum input pressure in order to prevent any prominent radial expansion that might cause actuator failure. Te actuator’s geometrical parameters were Li = 155 mm, wr = 5.0 mm, α =−30°, wi = 46 mm, wz = 0.0 mm, and nr = 16. Te FEM model predicts the twisting angle of the actuator well, with an RMSE of 4.94°. Based on previous work with fber reinforcements82, the twisting capability of the actuator, clockwise or counterclockwise (|α|), improves gradually from 0 to 30° and then reduces until α|=90, where the reinforcements are symmetric pre- venting the actuator from twisting and promoting just radial expansion. For the blocked torque capability, the FEM model predicts lower torque values up until around 50–60% of the simulation, where the payload of the experimental results match the simulation results very closely with an RMSE of 0.0352 Nm⋅ .

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Figure 6. Comparisons of sof actuators for fnger assistance. (a) [Lef] Highlights the diferent actuators worn on a user’s hand. [Right] Te diferent types of actuators defated and infated. i) Knitted fabric actuator, (ii) elastomeric actuator, and (iii) woven fabric actuator. (b) Angle v.s. pressure for three diferent actuators. c) Load v.s. pressure for three diferent actuators.

Case study of FSPAs in wearable applications One of the popular assistive/rehabilitative application for SPAs has been sof robotic gloves for patients sufering with reduced hand functionality8–10. We demonstrate the capabilities of the woven FSPAs and the knit FRTAs in comparison with the existing fiber-reinforced elastomeric actuators10, for finger flexion, as seen in Fig. 6a. According to literature, the requirements for fexion of the human index fnger10 includes a bending angle of at least 160° and a distal tip force of approximately 7.3N. Computational models of the FSPAs are modeled using the same geometrical parameters of the fber-reinforced elastomeric actuator10, in order assess the design before fabrication. Te common geometrical parameters for the actuators are Ra = 10 mm, wz = 10 mm, Lmi = 155 m. Te woven non-stretch actuators has na = 19, sp = 9 mm and wa = 20 mm and ha = 20 mm. Te knitted stretch actuators has nr = 35, wr =.135 mm, and sp =.15mm. Te FEM models are experimentally validated for bending angles and tip force payloads, while infating the specimens up to 0.206 MPa with a small pressure increment of 0.034 MPa, as seen in Fig. 6b,c. Both the fabric-based actuator FEM models meet the motion and force requirements. Te distal tip forces of the fabric-actuators obtained both through the FEM simulation are experimentally validated, resulting in an RMSE of 0.59 N and 0.49 N, for the woven FSPA and knit FRTA respectively. Both the experimental and FEM model data demonstrated similar bending behavior with an RMSE of 26.2° for the woven FSPA and 10.16° knit FRTA as seen in Fig. 6b. Te woven FSPA prototype displays an initial bending angle because of the stifness due to plastic fttings assigned to each actuator. From Fig. 6a and Supplementary Video 3, we compare the bending angles and distal tip forces of the three actuators together. Te woven FSPA instantly bends and curls when pressurized and reaches its maximum bending angle, at 0.069 MPa, which is approximately 1.7 × larger than the silicone and stretch fabric actuators’ bending angles. Terefore, this actuator reaches it’s maximum bending angle the quickest. On the other hand, the FRTA and fber-reinforced actuators steadily reach similar maximum bending angles at 0.206 MPa. Te silicone actuator also display a slight initial bending angle because the initial stifness exhibited by the material’s stifness, with a Hardness Shore 28A. As seen in Fig. 6c, the fabric-based actuators demonstrate approximately a 1.71 × higher payload at 0.206MPa, meeting the distal force requirements for the task at a lower operating pressure. Te silicone actuator needs to be pressurized till 0.275 MPa to meet the desired tip force. In terms of weight, the silicone, woven FSPA and knit FRTA actuators are 37.5 g, 82.5 g, and 9.7 g respectively (with pneumatic fttings). Te additional weight of the woven non-stretch fabric is due to the pneumatic fttings on each actuator in the array. Terefore, the FRTA actuators show the highest force-to-weight ratio in comparison to the other actuators. A prototype of the assistive wearable glove made of the FRTAs is presented in Supplementary Fig. 2. We further characterized these three actuators for their frequency response and efficiency, as seen in Supplementary Materials. For the frequency test, we noticed that the fber-reinforced elastomeric actuator, knit fabric-reinforced textile actuator, and woven fabric FSPA had the frequency response of 2 Hz, 0.7 Hz, and 0.45 Hz, respectively. Tis is highlighted in Supplementary Fig. 4 and Supplementary Video 5. We also analyzed the external energy interactions, based on83,84, of these actuators as seen in Supplementary Figs. 5 and 6. From the overall efciency tests, the elastomeric actuator, woven FSPA, and knit FRTA have maximum efciencies of 0.785% at 0.05 kg, 0.287% at 0.1 kg, and 0.26% at 0.2 kg, summarized in Supplementary Table 4. Discussion and Conclusion In this paper, we explored the combination of various textiles to mechanically program actuators to perform dif- ferent motion profles, while still being lightweight, compliant, and safe. We introduced two main classes of ver- satile fabric-based sof pneumatic actuators, the woven non-stretch fabric actuators and the knit fabric reinforced textiles actuators. Te woven fabric actuators used the interaction of multiple actuators arranged in diferent array fashions to create various motion profles. On the other hand, the FRTAs perform a combination of motions by utilizing the interaction of the woven fabric-reinforcements along the length of the mechanically anisotropic knit high-stretch fabric body. Both types of FSPAs demonstrated the potential to deliver signifcant blocked forces and displacements in comparison to the conventional fber-reinforced elastomeric actuators without introducing any mechanical instability, while still being highly wearable, lightweight, compliant, and safe. However, preliminary

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frequency testing has shown us that due to the fabrics’ pliability and thin-walled material properties, it shows a lower maximum operable frequency in comparison to the fber-reinforced elastomeric actuators. From the preliminary efciency tests, the relatively thick walled fber-reinforced elastomeric actuators show a higher efciency when lower work is done, but all three actuators show similar efciency at higher work. To improve the time-consuming limitations with manufacturing ofen seen in SPAs, we presented rapid and low-cost 2D manufacturing methods to develop these FSPAs using commercially available fabrics. Tese external fabric reinforcements that create a meta-material frame are designed accurately with any varying geometrical parameters, and perfectly aligned around the anisotropic textile body of the FRTAs. Te manufacturing method can be easily scaled and can produce even more complex geometries to beneft any assistive and rehabilitative tasks. We also comprehensively studied and mechanically characterized the various fabrics used to generate non-linear constitutive material models for large deformations based on the HGO form79 using bi-directional stress and strain data representing the mechanical anisotropy of the material. We implemented an extensive library of experimentally validated, FEM models for FSPAs (4 woven and 3 knit FSPAs). Tese models can be utilized as design tools for the users to vary the actuator’s geometrical parameters and materials, in order to predict the mechanical response of the actuators to internal quasi-static and dynamic pressure, as well as external contact. Tis will benchmark the design criteria for developing scalable and customizable FSPAs based on the articulation performance requirement and desired payload prior to fabrication. We aim to add the capabilities of distributed, embedded fabric sensing technologies, to monitor the articulation of the actuators and the interaction with the users and environment. Future work will also investigate the design of the actuators with user ergonomic considerations. Some key considerations will include selection of attachment points on the body to distribute the load along with various feedback/feedforward control strate- gies. Further exploration of the dynamic and time-dependent responses and dynamic hysteresis, of the actuators would need to be evaluated for various pressurization patterns. Future work will include more in-depth and comprehensive frequency and efciency testing. For the frequency test, more variations of the duty cycle between pressurization and venting will be tested. Te overall frequency of the FSPAs can also be improved by increasing the inlet size of the connectors, to improve the fow in and out of the actuator. For the efciency test, the initial volume of the actuators will be accounted as well as the efciency of the actuators during dynamic motion. Te future models will also allow the users to evaluate and optimize the actuators based on efciency and volume considerations that tie into on-board portability considerations. Finally, future research will also include analytical models of the non-linear behaviors of the fabrics at large deformations using the FEM models in this work to provide a baseline necessary for analytical characterization of these actuators.

Received: 18 December 2019; Accepted: 16 April 2020; Published: xx xx xxxx

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PMID: 29182080. Acknowledgements Tis work was supported in part by the National Science Foundation under Grant CMMI-1800940. Te authors thank S. Poddar, I.I.B. Mohd, S. Saivimal, Z. Qiao, and S. Seidel for help with assistance in the fabrication of actuators, result analysis, and FEM modeling. Te authors thank Dr. Polygerinos for his contribution to the initiation of this work. Author contributions P.H.N. performed the numerical simulations, fabricated the prototypes, performed the experiments, performed the material characterization, wrote the programs for the computational and material ftting models, analyzed the results, and wrote the main manuscript text. W.Z. analyzed the results and contributed to the main manuscript text and discussions. Competing interests Te authors declare no competing interests.

Additional information Supplementary information is available for this paper at https://doi.org/10.1038/s41598-020-65003-2. Correspondence and requests for materials should be addressed to W.Z.

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